We extend an original lapped transform (LT) and use block-lifting factorization to get an extended block-lifting-based LT (XBL-LT). The block-lifting structure maps integer input signals to integer output signals and results in a reversible transform that reduces rounding errors by merging many rounding operations. Although other such block-lifting-based LTs (BL-LTs) have been proposed, they are forcibly constrained by the use of discrete cosine transform (DCT) matrices. In contrast, XBL-LT is DCT-unconstrained and hence also embodies the DCT-constrained form. Furthermore, it has fewer rounding operations by merging the scaling factor with block-lifting coefficients. The both DCT-constrained and unconstrained XBL-LTs perform well at lossy-to-lossless image coding which has scalability from lossless data to lossy data.